Introduction

dS2 is a distributed hydrological model, based on the model defined by Kirchner (2009). The model assumes that the simulated discharge is solely dependent on the storage of that particular area. This model allows the user to apply this concept in a distributed fashion, where the spatial resolution is determined by the input files. The temporal resolution can be modified by the user as well.

Requirements

• Python 3.6, including basic libraries, such as: datetime, glob, os, pickle
• NumPy (1.16.2)
• pandas (0.24.1)
• xarray (0.11.3)
• tqdm (4.31.1)

Notes

All forcing input files should be entered as mm h-1, even if a coarser temporal resolution is used.

Input

Both input and output directories can be relative to the current model path, or direct to another directory using the full path name.

Name	Description	Unit	Notes
Precipitation	Precipitation values per pixel per time step	mm h-1	-
Evaporation	Evaporation values per pixel per time step	mm h-1	-
Temperature	Temperature per pixel per time step	mm h-1	Only for snow
Catchment	Map indicating the location of each (sub)basin, indices corresponding to outlet, main outlet must be "1.0"	-	2D ASCII file, where pixels outside the catchment are indicated with a NaN
Distance	Map with the distance of each pixel to the main outlet, via the stream network	m	2D ASCII files, pixels outside the catchment are indicated with a NaN
routingInfo.pkl	Pickle object with 3 dictionaries: outletLoc, catchLoc, outletInfo	-	See below

routingInfo.pkl:

• outletLoc: dict with outletID as keys, and the 1D cell number of the outlet location
• catchLoc: dict with outletID as keys, and the 1D cell numbers of all pixels within that subcatchment
• outletInfo: dict with outletID as keys, and a list as value with two items:
  • Downstream outletID
  • Distance to downstream outletID [m]

Parameters and settings

Name	Description	Example value	Unit	Notes
alpha	gQ parameter - intersect	-1.171	-	-
beta	gQ parameter - slope	0.57	-	-
gamma	gQ parameter - curvature	-0.03	-	If set to zero, gQ function is equal to original power-law a*Q^b
eps	ET - Reduction factor for ET	0.89	-	-
tau	Routing - Average velocity of water	2	m s-1	Average velocity of water to travel from a point to the outlet via the river network
Qt	ET - Minimum discharge value for ET	1e-4	mm h-1	If Qt+1 is expected to cross this threshold, ET is set to zero for these pixels
T0	Snow - Critical temperature for snowfall and melt	0	deg C	-
ddf	Snow - Degree day factor for snowmelt	2.00	mm day-1 degC-1	Value is corrected for dt
rdf	Snow - Radiation day factor for snowmelt	0.26	mm day-1 (W/m2)-1	Value is corrected for dt
dt	Stability - Size of timestep in hours	1	h	If timestep coarser than 1 hour, specify here
max_RAM	Stability - Maximum RAM the model can use	1024	MB	Chunksize per file is determined by the model options
size_one_value	Stability - Size of a single value	4	bytes	float32: 4 bytes, float64: 8 bytes
LB	Stability - Lower boundary for solver	1e-3	-	Factor determining the minimum value for Qt+1 (Qt * LB)
max_gQ_difference	Stability - Maximum allowed difference in gQ values	2	-	Difference is calculated based on abs(g(Q)_t2 - g(Q)_t1) / min(g(Q)_t2 - g(Q)_t1)
dt_reduction	Stability - Factor controlling the reduction in dt	0.15	-	The new timestep is based on the order of magnitude difference between gQ, to the power of this value
min_extra_dt	Stability - Number of minimum extra dt per dt	5	-	Parameter controls the minimum of internal timestep per dt
max_extra_dt	Stability - Number of maximum extra dt per dt	50	-	Parameter controls the maximum of internal timestep per dt

Explanation of scripts

• dS2_model.py: Main model code
• dS2_settings_and_run.py: File with model settings and example code to run the model
• funcFluxes.py: Functions for snowmelt and evaporation
• funcParams.py: Function to change parameters, with correction for units
• funcRouting.py: Functions required for routing
• funcSolver.py: Functions for both the RK4-approach with flexible dt, and the textbook Cash-Karp approach
• readInput.py: Functions to read settings class, and other file formats
• readOutput.py: Functions to write memmap files and translate memmap to NetCDF file

References

Buitink, J., Melsen, L. A., Kirchner, J. W., and Teuling, A. J. (2020), A distributed simple dynamical systems approach (dS2 v1.0) for computationally efficient hydrological modelling at high spatio-temporal resolution, Geoscientific Model Development, 13, 6093–6110, https://doi.org/10.5194/gmd-13-6093-2020.

Kirchner, J. W. (2009), Catchments as simple dynamical systems: Catchment characterization, rainfall-runoff modeling, and doing hydrology backward, Water Resources Research, 45, W02429, https://doi.org/10.1029/2008WR006912.